Question

A fez, the cap used by the Turks is shaped like the frustum of a cone. If its radius on the open side is 10 cm, the radius at the upper base is 4 cm and its slant height is 15 cm, find the area of the material used for making it.

(a) 210π cm² 

(b) 226π cm² 

(c) 326π cm² 

(d) 341π cm²

Answer 1

Answer: (b) = 226π cm²

For the fez, 

height (h) = 15 cm, r₁ = 4 cm, r₂ = 10 cm 

Total curved surface area of the fez = Lateral surface area of the frustum + Area of upper closed end

= π(r₁ + r₂)l + πr₁² = π{(4 + 10) × 15} + π.16 

= (210π + 16π) cm² 

= 226 π cm².